Finite Group Databasebeta

← #14795030

Subgroups — #14795030

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622460C211yesmaximal, characteristic, complemented
2#13076926C211yesmaximal, characteristic, complemented
3C4×#66983C211yesmaximal, characteristic
4#13070049C211yesmaximal, characteristic, complemented
5#13070039C211yesmaximal, characteristic, complemented
6#13069806C211yesmaximal, characteristic
7#13069799C211yesmaximal, characteristic
8#13069571C211yesmaximal, characteristic, complemented
9#13069386C211yesmaximal, characteristic, complemented
10#13069359C211yesmaximal, characteristic, complemented
11#13069354C211yesmaximal, characteristic, complemented
12#13069313C211yesmaximal, characteristic, complemented
13#13069313C211yesmaximal, characteristic, complemented
14#13068627C211yesmaximal, characteristic, complemented
15C2×C11×#432C211yesmaximal, characteristic, complemented
16C22×C42×C11C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×C4×C22⋊D11—21no—
19C2×C4×D44C2211yescharacteristic
20C2×#66923C2211yescharacteristic
21C11×#432—24no—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28#10622826—21no—
29#10622825C2211yescharacteristic
30#10622825C2211yescharacteristic
31#10622825C2211yescharacteristic
32#10622823—21no—
33#10622823—21no—
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66882C2211yescharacteristic
39C2×#66882C2211yescharacteristic
40C2×#66881C2211yescharacteristic
41C2×#66881C2211yescharacteristic
42#10622553—21no—
43#10622552C2211yescharacteristic
44C4×(C2×D11)⋊C4—21no—
45#10622549C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47#10622546—21no—
48#10622546—21no—
49#10622541C2211yescharacteristic
50#10622541C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622460—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C42×C11—22no—
72C2×C42×C11—22no—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80#66983—22no—
81#66983—22no—
82C4×C22⋊D11—44no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C4×D44—22no—
101C4×D44—22no—
102#66923—22no—
103#66923—22no—
104C11×C4⋊C8—22no—
105C11×C4⋊C8D414yescomplemented
106C11×C22⋊C8—22no—
107C11×C22⋊C8—22no—
108C11×#97—22no—
109C11×#97—22no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119#66885—22no—
120#66885—22no—
121#66885—22no—
122#66885—22no—
123#66882—22no—
124#66882—22no—
125#66881—22no—
126#66881—22no—
127#24706—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—24no—
149C2×C22⋊D11—42no—
150C2×C22⋊D11—42no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44#4112yes—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C2×D412yes—
178C2×C8×C11C2×D412yes—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11C2×D412yes—
184C42×C11#4112yes—
185C22⋊Dic11—42no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11#4112yes—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211C4×Dic11—42no—
212C2×#478—111no—
213C2×#432D1111yescharacteristic, complemented
214#2851—111no—
215C4×#121—111no—
216#2077—111no—
217#2075—111no—
218#2034—111no—
219#2033—111no—
220#1989—111no—
221#1949—111no—
222#1944—111no—
223#1943—111no—
224#1936—111no—
225#1936—111no—
226#1804—111no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11AGL(1,ℤ/8)12yes—
234C23×C11C22×D411yescharacteristic
235C22×D11—22no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11#12112yes—
262C2×C4×C11#12112yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C22⋊D11—48no—
270C2×Dic11—22no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291D44—22no—
292D44—22no—
293D44—41no—
294D44—41no—
295C4×D11—84no—
296C8×C11—22no—
297C8×C11—22no—
298C8×C11—41no—
299C8×C11—41no—
300C2×#125—111no—
301C2×#121—111no—
302C2×C4×D4—111no—
303C2×C4×D4—221no—
304C22×C42C2×D1111yescharacteristic
305#478—224no—
306#432—24no—
307C2×#107—111no—
308C2×#107—111no—
309C2×#106—111no—
310C2×#106—111no—
311C2×C4⋊C8C2×D1111yescharacteristic
312C2×C4⋊C8C2×D1111yescharacteristic
313C2×#102—111no—
314C2×#102—111no—
315C2×#102—111no—
316C2×#102—111no—
317C2×C22⋊C8C2×D1111yescharacteristic
318C2×C22⋊C8C2×D1111yescharacteristic
319C2×#97C2×D1111yescharacteristic
320C2×#97C2×D1111yescharacteristic
321#390—111no—
322#389—111no—
323#389—111no—
324#389—111no—
325#388—221no—
326#387—221no—
327#387—221no—
328#386—221no—
329#385—221no—
330#385—221no—
331#382—111no—
332#380—111no—
333#380—111no—
334#380—111no—
335C4×C4⋊C4—111no—
336C4×C22⋊C4—221no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345C22×C11—22no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11C2×#12111yescharacteristic
353C22×C11#52511yescharacteristic
354C22×C11#53611yescharacteristic
355C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C11#57511yescharacteristic
357C22×C11#57511yescharacteristic
358C22×C11#57511yescharacteristic
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C4×C11—22no—
367C4×C11—22no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11#54711yescharacteristic
372C4×C11#54811yescharacteristic
373C4×C11#55211yescharacteristic
374C4×C11#55611yescharacteristic
375Dic11—42no—
376Dic11—81no—
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380Dic11—81no—
381Dic11—81no—
382C22×D4—111no—
383C22×D4—221no—
384C23×C4—221no—
385C23×C4D4411yescharacteristic
386C23×C4D4411yescharacteristic
387C23×C4C22×D1111yescharacteristic
388C22×C8C22×D1111yescharacteristic
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392#125—222no—
393#125—222no—
394#121—222no—
395#121—222no—
396C4×D4—222no—
397C4×D4—222no—
398C4×D4—444no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—221no—
421C2×C42D4411yescharacteristic
422C2×C42D4411yescharacteristic
423C2×C42C22×D1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425#107—222no—
426#107—222no—
427#106—222no—
428#106—222no—
429C4⋊C8—22no—
430C4⋊C8C22⋊D1114yescomplemented
431#102—222no—
432#102—222no—
433#102—222no—
434#102—222no—
435C22⋊C8—22no—
436C22⋊C8—22no—
437#97—22no—
438#97—22no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448C2×C11—42no—
449C2×C11#241511yescharacteristic
450C2×C11#305411yescharacteristic
451C2×C11#305511yescharacteristic
452C2×C11#311111yescharacteristic
453C2×C11#311411yescharacteristic
454C2×C11#323411yescharacteristic
455C2×C11#324011yescharacteristic
456D11—82no—
457C24—221no—
458C24C2×D4411yescharacteristic
459C2×D4—112no—
460C2×D4—224no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—442no—
467C2×D4—442no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4C2×D4411yescharacteristic
491C22×C4C2×D4411yescharacteristic
492C22×C4C2×D4411yescharacteristic
493C22×C4C2×D4411yescharacteristic
494C22×C4C2×D4411yescharacteristic
495C22×C4C23×D1111yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8C2×C22⋊D1112yes—
507C2×C8C2×C22⋊D1112yes—
508C4⋊C4—112no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C22⋊C4—224no—
528C22⋊C4—442no—
529C22⋊C4—442no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C42—22no—
535C42—22no—
536C42—21no—
537C42—21no—
538C42—442no—
539C42#433912yes—
540C42C2×C22⋊D1112yes—
541C11#2470611yescharacteristic, complemented, Sylow
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—222no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23#6696112yes—
556C23C22×D4411yescharacteristic
557D4—222no—
558D4—222no—
559D4—448no—
560D4—441no—
561D4—441no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—222no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—884no—
603C2×C4#6698312yes—
604C2×C4#6698312yes—
605C2×C4C2×#433911yescharacteristic
606C2×C4#41×D1111yescharacteristic
607C2×C4#41×D1111yescharacteristic
608C2×C4#6704311yescharacteristic
609C2×C4#6704311yescharacteristic
610C2×C4C22×C22⋊D1111yescharacteristic
611C8—22no—
612C8—22no—
613C8—41no—
614C8—41no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—442no—
623C22—442no—
624C22—442no—
625C22—881no—
626C22—881no—
627C22—881no—
628C22—881no—
629C22#1062305511yescharacteristic
630C22#1062305711yescharacteristic
631C22C2×#6696111yescharacteristic
632C22#1062327911yescharacteristic
633C22#1062327911yescharacteristic
634C22#1062327911yescharacteristic
635C22C2×#6698311yescharacteristic
636C4—22no—
637C4—22no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—442no—
642C4—881no—
643C4—881no—
644C4—881no—
645C4—881no—
646C4—881no—
647C4—881no—
648C4#1062306011yescharacteristic
649C4#1062306411yescharacteristic
650C4#1062335511yescharacteristic
651C4#1062336211yescharacteristic
652C2—42no—
653C2—882no—
654C2#1307203911yescharacteristic
655C2#1307822511yescharacteristic
656C2#1307823511yescharacteristic
657C2#1307872711yescharacteristic
658C2#1307875611yescharacteristic
659C2#1307980811yescharacteristic
660C2#1307985811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#432C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#432D11
hypocenterC11#24706
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10622460C2semidirect
2. #13076926C2semidirect
4. #13070049C2semidirect
5. #13070039C2semidirect
8. #13069571C2semidirect
9. #13069386C2semidirect
10. #13069359C2semidirect
11. #13069354C2semidirect
12. #13069313C2semidirect
13. #13069313C2semidirect
14. #13068627C2semidirect
15. C2×C11×#432C2semidirect
105. C11×C4⋊C8D4semidirect
213. C2×#432D11semidirect
430. C4⋊C8C22⋊D11semidirect
541. C11#24706semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106224602
#130769262
C4×#669832
#130700492
#130700392
#130698062
#130697992
#130695712
#130693862
#130693592
#130693542
#130693132
#130686272
C2×C11×#4322
#2470611